Water and Ice

When water changes into ice, the volume increases by one ninth. Consider a 20 cm-tall cylindrical beaker, full of ice. On top of the beaker, there is a cone of ice of the same diameter and 5 cm-tall. When all the ice melts into water, what is the height of the water in the beaker?

Hint

Answer

When water changes into ice, the volume increases by one ninth. This means that the ratio of the volumes of water and ice is 9:10.

A 5 cm-tall cone of ice is as large as a 5/3 cm-tall cylinder, which makes a total of 20+5/3=65/3 cm of ice, and will yield 65/3*9/10=19.5 cm of water. Because 19.5<20, the cylinder itself can hold all the water, and the cone is emptied. Therefore, the height of water is 19.5 cm.Hide